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Design patterns - Singleton and class loaders

The Head First design patterns book mentions singletons and class loaders.
Question : What about class loaders? I heard there is a chance that
two class loaders could each end up with their own instance of
Singleton.
Answer : Yes, that is true as each class loader defines a namespace.
If you have two or more class loaders, you can load the same class
multiple times (once in each classloader). Now, if that class happens
to be a Singleton, then since we have more than one version of the
class, we also have more than one instance of the Singleton. So, if
you are using multiple classloaders and Singletons, be careful. One
way around this problem is to specify the classloader yourself.
In which situation do Java developers need to have multiple class loaders ? In which situations would multiple class loaders be a problem for singletons ?

Will extending a class load up memory?

In the application i'm trying to build, I have a utility class which I'm extending to use the utility methods present within.
#Repository("userdao")
public class UserDAO **extends baseDAO**{
private float PROFILE_FIELD_COUNT=16.0f;
List<UserProfile> ObjList=null;
...
...
...
My question is that will this extension load up all the methods into the memory? Or is it better to instantiate an object for the base class and use the methods through that object? Which is light-weighing in terms of memory consumption?

Extending another class (such that there are two classes) is no different in terms of practical memory usage1 than creating two distinct classes which are both used. Likewise, the "depth" of the extension tree does not affect the memory usage of instances.
The "memory cost" of multiple classes is inconsequential in all but the most limited embedded environments: write the cleanest cost. Independent of the choice of subtyping (it may be better to share "utility methods" through Dependency Injection and Composition), trying to cram everything into a single "DAO class" is likely wrong.
1 There is a difference, see Java Objects Memory Structure and will depend on the particular implementation.

How java ensures only one instance of an enum per JVM

How does Java ensure internally that only one instance of an ENUM would exist per JVM? Is it created when application boots up and from that point on when multiple threads access it, it will just return the object created at startup?
Or does it implement some kind of double synchronization similar to the singleton pattern so that even if multiple threads access it, only one istance will be created?

as you can read in this answer enum instances are static class fields and so are initialized as part of class loading when you 1st access the class.
classloading is synchronized internally so that ensures enum instances are singletons (singletons within the same classloader, that is. if you have the same enum loaded by multiple loaders you will get multiple instances)

Enum instances are created at class loading time. If the same enum gets loaded by more than one classloader (when classloading games are being played by, for example, a web app container), you will have multiple incompatible instances in memory.

Singleton objects and Java servlets

When I access a singleton Java object from withing a servlet, that object is only "single" or "one instance" for the give servlet thread or single throughout the JVM on the Server OS (like Linux)?
I mean when client connects to the servlet/service, are singleton object are unique to each thread created for each client or its unique throughout the whole JVM installed in the machine?

I think the object is unique for each user, not to the whole JVM. The only persistent information is the one you put in the user session.
I'm not sure, but I think you can acomplish to have one instance of a Class in the whole Application Server using the ClassLoader class, however I don know how it's done.
UPDATE:
Taken from the Java Article "When is a Singleton not a Singleton?"
Multiple Singletons Simultaneously Loaded by Different Class Loaders
When two class loaders load a class, you actually have two copies of the class, and each one can have its own Singleton instance. That is particularly relevant in servlets running in certain servlet engines (iPlanet for example), where each servlet by default uses its own class loader. Two different servlets accessing a joint Singleton will, in fact, get two different objects.
Multiple class loaders occur more commonly than you might think. When browsers load classes from the network for use by applets, they use a separate class loader for each server address. Similarly, Jini and RMI systems may use a separate class loader for the different code bases from which they download class files. If your own system uses custom class loaders, all the same issues may arise.
If loaded by different class loaders, two classes with the same name, even the same package name, are treated as distinct -- even if, in fact, they are byte-for-byte the same class. The different class loaders represent different namespaces that distinguish classes (even though the classes' names are the same), so that the two MySingleton classes are in fact distinct. (See "Class Loaders as a Namespace Mechanism" in Resources.) Since two Singleton objects belong to two classes of the same name, it will appear at first glance that there are two Singleton objects of the same class.

I'd say it depends on how the singleton is implemented, but all requests for a given app execute in the same VM, so it should be one instance for all requests.
EDIT: This is assuming a straight-forward Singleton implementation similar to:
public class MySingleton {
private static MySingleton _instance;
// for sake of simplicity, I've left out handling of
// synchronization/multi-threading issues...
public static MySingleton getInstance() {
if (_instance == null) _instance = new MySingleton();
return _instance;
}
}

Yes it is Singleton. But the scope of the singleton depends on where the class is located.
If it is located inside application, it is singleton for that application. If the same class is present inside another application then another object is created for that application and it is singleton for that application.
If it is located outside application and within server, it is singleton for the VM.

According to this
https://tomcat.apache.org/tomcat-8.0-doc/class-loader-howto.html
every Web application has it's own class loader, so the singleton will be unique for one application and it can't be visible to another

When you create a Singleton instance, all request instances will share the same instance for the current class loader it uses.

Since all the Servlets run on a webserver which runs on a single JVM, there will be only a single Singelton Object for all your servlets.

Static variables restriction in session beans

It's impossible to use static variables on a session bean code. Is this restriction arbitrary or fundamented? And why?
Best regards

As stated in the FAQ on EJB restrictions, one of the restrictions for using EJBs is:
enterprise beans should not read or write nonfinal static fields
Further expanded in the discussion on static fields:
Nonfinal static class fields are disallowed in EJBs because such fields make an enterprise bean difficult or impossible to distribute. Static class fields are shared among all instances of a particular class, but only within a single Java Virtual Machine (JVM). Updating a static class field implies an intent to share the field's value among all instances of the class. But if a class is running in several JVMs simultaneously, only those instances running in the same JVM as the updating instance will have access to the new value. In other words, a nonfinal static class field will behave differently if running in a single JVM, than it will running in multiple JVMs. The EJB container reserves the option of distributing enterprise beans across multiple JVMs (running on the same server, or on any of a cluster of servers). Nonfinal static class fields are disallowed because enterprise bean instances will behave differently depending on whether or not they are distributed.
It is acceptable practice to use static class fields if those fields are marked as final. Since final fields cannot be updated, instances of the enterprise bean can be distributed by the container without concern for those fields' values becoming unsynchronized.

It is fundamental. As per this sun documenation,
Nonfinal static class fields are disallowed in EJBs because such fields make an enterprise bean difficult or impossible to distribute. Static class fields are shared among all instances of a particular class, but only within a single Java Virtual Machine (JVM). *

static means unique for a class OR for all it's objects.
Now, javabeans are supposed to have user-specific data, static fields don't make any sense for these.
One user edits a variable, ant it'll be updated for all other users too. (at free of cost :-)).
However if you want static behaviour for these (i.e. using same data for all users), you have application for that purpose.